(1/4-x^2)=0

Solution for (1/4-x^2)=0 equation:

(1/4-x^2)=0


Domain of the equation: 4-x^2)!=0

We move all terms containing x to the left, all other terms to the right

-x^2)!=-4

x!=-4/1

x!=-4

x∈R


We get rid of parentheses

-x^2+1/4=0

We multiply all the terms by the denominator


-x^2*4+1=0

Wy multiply elements

-4x^2+1=0

a = -4; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-4)·1
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4}{2*-4}=\frac{-4}{-8}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4}{2*-4}=\frac{4}{-8}
=-1/2
$